Stereological techniques for Solid TexturesJan Tore Stølsvik

Overview● Goal● Why● Stereology● Solid Textures● Estimating 3D Distributions● Reconstructing the Volume● Results● Conclusions

Goal● Automatic Texture mapping for arbitrary

shapes ● Textures with particle distribution like

asphalt, rocks and also sponges (particles are void space)

● Should require 2D image input of material only

● Show Video

Why● It is a difficult and tedious task to get multiple 2D

textures to form a consistent visual appearance on a model without it looking bad

● 2D texture synthesis works bad for objects cut out of 3D spatially varying materials

● For use in computer graphics applications

Stereology● Used in biology and material science● Try to guess the 3D shapes of a cross

section

Solid Textures● Make an object you want to texture● To render this object each pixels gives its 3D position to

the algorithm which tells it the color it should have● It is difficult and tedious to get multiple 2D textures to

form a consistent visual appearance on a model without looking bad.

Estimating 3D Distribution● As in stereology, but we try to estimate the

distribution of different particles in a medium from a 2D slice

● Our objective is to establish a relationship between the size distribution of 2D circles in circles pr unit area and 3D spheres in spheres pr unit volume

● For any distribution of identical convex particles the particle density is expressed as

SpheresFor most volumes it is unlikely that the particles will all be of the same size, so we use a histogram approach

Other Particles● We cannot easily classify the profile size

according to its diameter● Kij represents the relative probability that a

particle in column j exhibits a profile in row i

Other Particles● To compute the K matrix they use the Monte Carlo

routine to take advantage of the GPU● Randomly orient the polygon mesh● Render such that the near clipping plane of an

orthographic camera cuts through the particle at random depth

● Read of the stencil buffer to find the area● Keep track of the biggest area● Record all these and create probabilities● Run around 100.000 times● Can also be used to find the mean caliper diameter

Other ParticlesBefore this data can be used we need a scale factor s to relate the size of particle P to the size of the particles seen in our input image

Aimg is the maximum area in the image and Amax is the Maximum area in our calculations

Calculate the H by multiplying s with the mean caliper diameter then solve as usual

Managing Multiple Particle TypesIf there are multible types of particles of different shape each particle type i will have its own mean caliper diameter, matrix Ki and distribution Nvi

We can assume that the distribution of size is independant of type, so we can express this as

where Nv is the sum of all Nvi’s and P(i) is the probability that particle p is of type i

Reconstructing the Volume● Once we have the particle densities Nv a

volume can be constructed, the process establishes particle positions and colors

● Create particles according to the distribution● Place all the particles inside a volume● Run simulated annealing to resolve

collisions● This repeatedly searches for all collisions

and then relaxes particle positions to reduce collisions

Reconstructing the Volume● If size and color are uncorrealated then

assign colors to the particles randomly● If this is not the case use a k-means

clustering algorithm to set the mean profile colors. Then run the stereology algorithms on each color and then combine the results

● To add fine details the mean is subtracted from the original picture and an existing similar method is used to add these details

Results● Recreation of synthetic volumes, very successful● Work with physical data was hard because the

algorithm depends on you creating the particles you think will be in the volume

● Test volume, they carved a shape out of real material and challenged the algorithm to do the same

● Physical inputs, they tried to replicate simple 2D pictures of materials

Conclusions● The methods expand on the class of 3D

solid textures that can be synthesized from 2D photographs

● Building on stereology and existing literature the methods manage to perform accurate predictive rendering with a sound statistical approach

● Future work includes automated estimation of 3D particle shapes and support for greater variety of input textures